Tracking motion kinematics and tremor with intrinsic oscillatory property of instrumental mechanics

Abstract Tracking kinematic details of motor behaviors is a foundation to study the neuronal mechanism and biology of motor control. However, most of the physiological motor behaviors and movement disorders, such as gait, balance, tremor, dystonia, and myoclonus, are highly dependent on the overall momentum of the whole‐body movements. Therefore, tracking the targeted movement and overall momentum simultaneously is critical for motor control research, but it remains an unmet need. Here, we introduce the intrinsic oscillatory property (IOP), a fundamental mechanical principle of physics, as a method for motion tracking in a force plate. The overall kinetic energy of animal motions can be transformed into the oscillatory amplitudes at the designed IOP frequency of the force plate, while the target movement has its own frequency features and can be tracked simultaneously. Using action tremor as an example, we reported that force plate‐based IOP approach has superior performance and reliability in detecting both tremor severity and tremor frequency, showing a lower level of coefficient of variation (CV) compared with video‐ and accelerometer‐based motion tracking methods and their combination. Under the locomotor suppression effect of medications, therapeutic effects on tremor severity can still be quantified by dynamically adjusting the overall locomotor activity detected by IOP. We further validated IOP method in optogenetic‐induced movements and natural movements, confirming that IOP can represent the intensity of general rhythmic and nonrhythmic movements, thus it can be generalized as a common approach to study kinematics.

rhythmic and nonrhythmic movements, thus it can be generalized as a common approach to study kinematics. Therefore, current technology of motion tracking focuses on the high-definition tracking of one limb or one targeted motion. However, many motor phenomena, such as reaching movement, walking, or balancing, involved complex coordinated movement beyond the limb being studied. For example, the cerebellum engages different functions for walking when two legs in human (or two sides of limbs in mice) move in the same versus different cycling speed. [1][2][3][4] This has been the foundation of cerebellar-based motor learning and rehabilitation after cerebral insults. 3,4 Adding to the complexity, most of the movement disorders behave very differently when volitional movement is involved. The dystonia severity is exacerbated, known as "overflow phenomenon," when the supported arm or trunk are also moving. 5,6 The intensity of tremor, which is an involuntary rhythmic movement, increases with bigger volitional movement. [7][8][9][10][11][12] There is a clear need for a technology to simultaneously track the motor kinematics of both targeted limb movement and overall motion.
To date, motion tracking depends on the camera for superior information of limb/body position, but it is limited by the data rate and restricted scenarios suitable for video capturing. 13,14 High-speed camera array provides better temporal resolution, but the more stringent illumination and imaging depth limit their applications to the scenario for freely volitional movement, which is critical to the manifestation of movement disorders such as tremor, dystonia, and myoclonus, and complex natural behaviors such as balancing and turning. Novel tracking techniques, like fluoroscope and skin-marker (optical marker) tracking system, provide further kinematics details to track specific motion but also face the limitations that traditional video methods suffer from. [15][16][17][18][19] In high-resolution scenarios, they are more sensitive to environmental settings and global motions, therefore limiting their application to head-fixed or restrained settings. Another option is accelerometer-based detection. Accelerometer has superior temporal resolution but is less capable of differentiating targeted movement from overall locomotor activity contributed by other body parts. [20][21][22] On the other hand, ultrasound-based motion tracking provides precise kinematics information for fine movements, but it is not designed to track free-moving global movements. 23 Besides, among the above-mentioned tracking techniques, only the traditional video methods and the accelerometer method are well established and affordable at the same time. Collectively, a high-precision, easy to use motion tracking system for movement disorders is still an unmet need.
Here, we introduce another method, intrinsic oscillatory property (IOP) of a harmonic oscillator, to measure overall momentum in a freely moving animal. Based on the basic mechanical principle of physics, intrinsic oscillation is a fundamental phenomenon existing in every rigid body attached to a spring. Any movement applied to the system will trigger the intrinsic oscillation, and the amplitude of this frequencyspecific vibration is proportional to the given force. Such system gener-   24 We also validated the IOP method for tracking motion kinematics beyond tremor, including optogenetic-induced movement and nonrhythmic natural movement. IOP method is shown to be capable of capturing overall kinematics of an animal under artificially induced motion. It is also shown to represent the global natural movement.
Collectively, the IOP method can be a useful tool for studying various motor phenomena. Adding to its superiority in tracking motion kinematics, its low-cost and easy-to-use characteristics make it a potential novel approach to advance our understanding of motion phenomena and motion disorders. We built a force plate with IOP (Figure 1a, formula). It is assembled by a basal plate, a loading cell, and a preamplifier (see Section 5 and Figure S1). To validate whether abovementioned physical property can be faithfully presented in the force plate and can be used in tremor recording, we first applied forces by mechanical tapping at 5 Hz, 7 Hz or nonperiodic random tapping (Figure 1a). During tapping, both periodic and nonperiodic forces generated intrinsic oscillations F I G U R E 1 Distinguishable frequencies between rhythmic activity and intrinsic oscillations that reflect overall motion. (a) Scheme of force plate-based motion detection with intrinsic oscillatory properties. The oscillatory frequency (f ) of a force plate depends on system stiffness (k) and mass (m), but not displacement (x) or acceleration (a (j) Reduction of coefficient of variation (CV) after IOP normalization. (n = 9 mice) *p < 0.05, Wilcoxon signed-rank test at $42 Hz, reflecting the natural frequency in our system (Figure 1b).
The oscillations went through fast attenuation and were not detectable during nontapping period. During periodic tapping, the force plate reliably detected the rhythmic motion at 5 Hz or 7 Hz (Figure 1b, magnified). The results suggest that IOP can be a reliable method for motion detection without compromising the ability to record the force rhythm. We also examined IOP with different masses on the force plate. The observed frequency was reduced when additional mass was applied on the plate (Figure 1c). Curve fitting on the frequency-mass dataset (Figure 1d) was highly consistent with the mechanical principle of physics (Figure 1a, formula). Taken together, IOP in a force plate can reliably capture both rhythmic and nonrhythmic force, and the oscillatory frequency can be tuned by adjusting the mass of the system.

| IOP-based motion detection for tremor measurement and normalization
To examine whether IOP can be used for quantitative motion detection with high temporal resolution and accuracy, we next applied action tremor as the model for kinematic measurement (Figure 1e).
We measured rhythmic activity in either wild-type mice or homozygous Grid2 dupE3 mice, which had action tremor at 20 Hz. 24 Intrinsic oscillations at 42 Hz were found in both wild-type and Grid2 dupE3 mice, while the tremor spectrum with the evidenced peak at 20 Hz was only detected in Grid2 dupE3 mice ( Figure 1f, red arrow). We next examined the correlation of intensity between intrinsic oscillations and tremor in Grid2 dupE3 mice ( Figure 1g). There was a strong linear correlation between tremor intensity and intrinsic oscillatory intensity.
As IOP reflects overall kinematic activity, this strong correlation is compatible with previous studies that tremor intensity is affected by overall locomotor activity. [7][8][9][10][11][12] Since tremor severity of a given animal is a state of the disease, it should be the same across trials and independent of the animal's locomotor activity, which modulates the raw intensity of action tremor Taken together, the IOP method can be a reliable method to measure overall momentum. Therefore, IOP can be used to normalize the action-dependent variability of tremor and generates a more stable readout indicating activity-adjusted tremor severity, which reflects a reliable proportion of tremor (tremor intensity) among overall motion (intrinsic oscillatory intensity).

| Comparison of IOP with video-based motion detection for tremor normalization
To evaluate the efficacy of IOP-based normalization for tremor, we first   [31][32][33] Interestingly, carbamazepine has no clinical benefit to essential tremor patients but has been reported to suppress mouse tremor. 34 This paradox leads to criticism of tremor animal models and creates substantial obstacles to evaluating new therapies for essential tremor in animal models.

| Comparison of IOP method with videoassisted, accelerometer-based tremor measurement
To validate whether IOP-determined tremor severity can be used for evaluating therapy for essential tremor, we applied clinically used medications for essential tremor to Grid2 dupE3 mice, including primidone, propranolol and ethanol. We compared IOP-normalized tremor intensity, which reflects tremor severity, before and after medication administration. We found that medications for essential tremor may

| IOP-based method detects optogenetically induced rhythmic movement in intact motor circuit
Although IOP-based method can be reliably applied to measure tremor in Grid2 dupE3 mice with abnormal cerebellar pathology, 24 it is unclear whether IOP-based method can also be applied to normal brain circuits for rhythmic or patterned movement. To address this issue, we optogenetically stimulated deep cerebellar nuclei (DCN) in wild-type mice (Figure 6a).

| IOP in quantifying nonrhythmic natural movement
The next question is whether IOP methods can also be used to study non-rhythmic movement? We thus examined IOP methods in measuring overall momentum of nonrhythmic, natural movement. We analyzed the light-off periods in the above-mentioned optogenetic experiments (Figure 7f). In these periods, mice showed their physiological movement in freely moving state without obvious brisk activity whose motion spectrum may fall into higher frequency ranges. We therefore integrated the 2-30 Hz data to represent the overall momentum. Our data showed a strong correlation between the overall momentum and the intensity of intrinsic oscillations at 42-50 Hz ( Figure 7g). The data suggested that IOP can be applied to quantify overall momentum in both rhythmic and nonrhythmic movement.
Therefore, kinematics studies targeting specific brisk movement (e.g., reaching for food) may be isolated and separable by overall momentum represented by the IOP-specific frequencies, which are tunable in the system to fit different experimental scenarios (Figure 1c,d).

| DISCUSSION
In this study, we identified the IOP method, which used intrinsic oscillations of a force plate to detect and quantify the overall momentum due to locomotion. Using tremor as a model, head-to-head compari- Here, we validated IOP as an additional method for kinematics study. Combination of IOP and other methods can be beneficial.
Although accelerometer-based tremor measurement in our setup seems inferior to force plate-based method, it could be due to a single accelerometer that detects the targeted motion, but not the overall momentum as the force plate measurement does. By combining the two methods, multiple miniature accelerometers attached to the head and limbs could provide detailed kinematics at multiple joints locally, and the coexisting IOP method could reflect global momentum and frequency integration of coordinated movement. Video is a nonreplaceable method to capture the moving types (e.g., grooming vs. walking). Combination of all methods may provide more comprehensive information for studying kinematics of movement.
In addition to the marker-less video capturing and accelerometerbased measurement, locomotion analysis has been performed with the aid of other techniques including skin-marker (optical marker) tracking system, fluoroscope, and ultrasound-based motion tracking. [15][16][17][18][19]23 Skin-marker tracking systems have been used in human and rodent gait analysis and have an advantage in marking joint position and angles. 15,16 However, there is also evidence that markerbased tracking systems can yield large error in estimated kinematics when applied to freely moving rodents. 18 Besides, marker-based video capturing may interfere with physiological behavior due to the marker placement and may reduce the versatility of pose estimation and kinematics analysis. 16 On the other hand, fluoroscope-based motion tracking can obtain internal bone structure with x-ray, which is more precise in tracking limbs kinematics compared with traditional video capturing. 18,19 However, animals have to be relatively fixed or restrained for this tracking technique, which may disturb their natural locomotion and the underlying neuronal activity. In addition to fluoroscopy, ultrasound has also been applied to motion tracking. It is relatively safe in comparison to the possible radiotoxicity that may be caused by fluoroscopy. This new technique has been used in tracking tendons, 23 and may have the potential of tracking fine movements in rodents. Nevertheless, such technique may also require the animal to be restrained while being scanned, and its anisotropy problem still awaits solutions. 23 Last but not least, although these techniques perform superiorly in motion tracking of specific limbs or finer structures, they are not designed to track overall motion kinematics, which is the gap that can be filled by our proposed IOP approach.
To solve the difficulty concerning the tracking of global motion kinematics, there have been ample studies on tracking multiple body parts at the same time. These approaches include the application of inertial sensors, 38,39 marker-based tracking, 40 and marker-less model tracking. 41 These novel approaches perform well on multiple body parts tracking and thus are good at capturing the whole-body postures. However, the dispersed nature of multiple body parts tracking still impedes it from integrating the diverse kinematics of each tracked body part into a single index of global motion kinematics. Besides, most of these multiple body parts tracking approaches rely on video capturing, 40,41 rendering them limited by the temporal and spatial resolutions problems as well as restrain-related issue confronting videobased tracking methods. Others rely on innovative inertial sensors tracking, but this approach requires researchers to design and build the sensor system on their own without a well-established and easyto-use protocol at present. 38 Hence, optimizations are indispensable for these approaches to be used in global motion kinematics tracking.
In comparison, our IOP approach using a force plate is relatively convenient to use, and is able to generate a single index for quantifying global motion and cater to the need of tracking in a timescale of milliseconds.
Additionally, to study the pathophysiology of motion disorders using freely moving animal models, it is imperative to determine whether symptom modulation is resulted from dampening the neuronal mechanisms responsible for the symptom (e.g., tremor generator in the central nervous system) or simply from a reduction of overall activity. Hence, constrained experimental scenarios, such as head-fixation or physical restraint, may affect action and therefore the expression of motor symptoms. In this context, IOP may provide a more natural way to record and calibrate motor deficits in a freely moving setting and thus yield higher ecological validity for studying neural mechanisms and therapeutics of motion disorders in humans.
Although our study has been performed on animal models, the force plate-based IOP approach also shows potential in translational human applications. Currently, force plate has been applied to evaluate balancing functions for physical therapy and for identifying individuals at risk of falling. 42,43 Assessment of neuromusculoskeletal function while standing or walking can also be performed on a force plate for patients with foot and ankle pathology. 44 With proper tuning of these clinical-used force plates, our IOP approach can further improve the quantification of these symptoms' severity. Furthermore, it may aid in the evaluation of motion disorders beyond existing applications. For example, IOP calibration of motor symptoms severity can be expanded to assessment of disorders like myoclonus, dystonia, and various types of tremor in the future. Moreover, symptom assessment is not only important for diagnosis of motion disorders but also crucial to evaluation of therapeutics. Hence, in addition to the applications in animal motor phenomena studies, our IOP approach also has the potential of clinical usage.
As demonstrated, IOP can be a useful approach to study tremor pathophysiology. Essential tremor, characterized by action-dependent tremor, is the most common movement disorder with unsatisfactory pharmacological therapies and poorly understood pathophysiology. As a result, essential tremor has been the model disease used for testing modern therapeutic technology, including deep brain stimulation and magnetic resonance-guided focus ultrasound. [45][46][47][48] Therefore, it is pivotal to establish a standard to evaluate the severity of tremor, which should be pathophysiologically related but independent of the highly variable motion states. Current studies have built up the standard protocols for clinical assessments to identify postural and action tremor. 49,50 However, calibration of tremor intensity in the context of global motor activity modulation requires further effort. Since force plate can faithfully and sensitively detect the force made by local muscular vibration, such as tremor, and IOP can summarize the overall motion of an indicated movement, we suggest that our method can be used to estimate the severity of motion disorder in a specific part of the body by comparing the force/energy imposed by the symptom to the overall force/energy arising from volitional locomotion.
Because we normalized the intensity of motion disorder to the overall motion, this method can provide an objective index in the face of the heterogeneity in human patients' symptom expressions.
In summary, the IOP approach is a low-cost and easy-to-use method for evaluation of motor phenomena and motor deficits. Using action tremor as an example disease model, this approach is shown to be capable of capturing the overall motion kinematics that modulate the expressed intensity of motor deficits. By taking advantage of its flexibility to adapt to various recording scenarios, the applications of the IOP method may be expanded to assessments of more motor phenomena and shed new light on human motion disorders in the future.

| CONCLUSIONS
In summary, we simultaneously compared force plate-based, accelerometer-based, and video-based detection of motion in freely moving mice. We demonstrated that the IOP of a force plate provides a more consistent measurement for the overall momentum of locomotion. A reliable method for measuring the overall activity is particularly critical to study the modulators of locomotion. For example, movement changed due to medication effect and neuronal circuitry activation. Combining detections of overall and targeted locomotion will advance the studies in behavior changes of freely moving mice in response to different modulatory elements that instantly affect neuronal circuitry.

| MATERIALS AND METHODS
Details are referred to Supplemental Methods S1.
All experiments were performed under the protocols approved by the IACUCs at NTU (B202000003) and CUIMC (AAAT7472). The connector for accelerometer was secured on the mouse skull. Optic fiber was implanted to the deep cerebellar nuclei (DCN; AP, À6.24 mm from bregma; ML, +2.1 mm from midline; DV, À1.9 mm from dura).

| Force plate assembly
A force plate with IOP ( Figure S1) was assembled by three components: a basal plate to support the free-moving mouse; a loading cell to provide both elasticity for spring effect and linear force-voltage transformation; and a preamplifier to transmit stable voltage readout ( Figure S1b,c). The load cell transfers the weight into voltage at the ratio of 33 mV per gram-gravity and the gain of the preamplifier is set to 1000Â. Thus, the temporal dynamics of the applied force or motion kinematics is transformed into continuous voltage output ( Figure S1d and Movie S1). With the existence of IOP, the energy given to the force plate becomes the source of oscillations and is further transformed into the oscillatory power at the intrinsic oscillatory frequency

| Mechanical tapping
Motion was generated by mechanical tapping on the force plate. Specific frequencies (5 and 7 Hz) were applied with the aid of metronome (Pro Metronome, EUMLab). To demonstrate that the force plate obeys the physical principle of IOP, objects with six different masses (0, 90, 190, 390, 590, and 880 g) were applied to the force plate and random tapping with varying force was applied. The resulting IOP frequency values were used for deriving the reciprocals of square of frequency (1/frequency 2 ). The relationship of these values with the corresponding weights was fitted by a linear curve and followed by correlation analysis.

| Tremor measurement settings and tremor recordings
While a mouse was freely moving on the force plate, accelerometer signals sampled at 1000 Hz and videos captured at 60 frame-persecond were recorded simultaneously. Mouse activity on the force plate was transduced into voltage signal at 1000 Hz. Headstage containing accelerometer was connected to the implant on the mouse's skull. Mouse's body center was determined by using DeepLabCut video processing. 51

| Accelerometer-based recording
Custom headstage containing an ADXL335 accelerometer (Analog Devices) was connected to the implant adhered on the mouse's skull during the recording. The accelerometer is three-dimensional and can measure acceleration with a minimum full-scale range of ±3 g. The sensor is a polysilicon surface-micromachined structure providing a resistance against acceleration forces. Deflection of the structure is measured using a differential capacitor, resulting in a sensor output, whose amplitude is proportional to acceleration. Phase-sensitive demodulation techniques are then used to determine the magnitude and direction of the acceleration. Signals were recorded and processed by Cerebus Neural Signal Processor (Blackrock Microsystem) and were digitized at 30 kHz.

| Video-based recording and tracking
Video recording was performed with uEye camera (IDS Image Developing Systems) from an above view. The video was recorded with the resolution of 1280 Â 720 pixels, covering the open field of 28 cm Â 16 cm, giving the pixel resolution of 0.22 mm in both X and Y direction. The frame rate was 60 frame per second (FPS). The mouse body center was identified by the free algorithm DeepLabCut. 51 Frameby-frame displacement was used to calculate the mice's moving velocity with the X and Y coordinates of the body center. The velocity data were then transformed into PSD data and subjected to further analyses. 5.7 | Signal preprocessing for power spectrum analysis and peak determination Signals from force plate-based, accelerometer-based, and video-based recording were aligned with a manually triggered analogue signal. This signal was sent to the electrophysiological system and lighted up a red LED at the same time. The electrical signal aided in aligning the time frame of force plate-and accelerometer-based recordings. The red LED was set at the margin of the video, aiding in the alignment of video recordings to the electrical signals. The aligned signals were analyzed by custom-written code in MATLAB. 24,52,53 Coordinates data from the video-based tracking, vector magnitudes from the accelerometer recording, and electrical signals from the force plate, were used for power spectrum analysis. Peak value in the power spectrum density (PSD)-frequency plot was determined by locating the local maximum of concave downward feature.

| Signal normalization
In force plate measurement, tremor PSD was normalized to summed PSD amplitude between 40 and 50 Hz (IOP of force plate) in the same period. For video data, tremor PSD data derived from moving velocity was normalized to general activity (overall 2-30 Hz PSD also derived from moving velocity) or moving velocity per se. PSD data derived from acceleration was normalized to general activity (overall 2-50 Hz PSD also derived from accelerometer) or moving velocity from video data. To avoid biased value due to small denominator (moving velocity), PSD data of a time point were ruled out if the corresponding moving velocity was not over the threshold of 0.4 mm/s.

| Medication in homozygous
Correlation analysis was applied to PSD in tremor frequency and IOP.
For other statistical analyses, Wilcoxon signed-rank test, Kruskal-Wallis rank sum test, Dunn's all-pairs test, and Friedman test were performed in RStudio. 54

| Optogenetic stimulation and the analysis of rhythmic movement induction
Optogenetic stimulation was given via a diode laser module with the indicated frequency and illuminating power (see Supplemental Methods S1). The induced motions were recorded on the force plate.